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H 0 Group structures of elliptic curves #2

Auteurs : Shparlinski, Igor
CIRM (Editeur )

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    Résumé : We give a survey of results which address the following generic question: How does a random elliptic curve over a finite field look like.
    This question has a rich variety of specfic interpretations, which depend on how one defines a random curve and what properties which are of interest. The former may include randomisation of the coefficients of the Weierstrass equation or the prime power defining the field, or both. The latter may include studying the group structure, arithmetic structure of the number of points (primality, smoothness, etc.) and certain divisibility conditions.
    These questions are related to such celebrated problems as Lang-Trotter and Sato-Tate conjectures. More recently the interest to these questions was re-fueled by the needs of pairing based cryptography.
    In a series of talks we will describe the state of art in some of these directions, demonstrate the richness of underlying mathematics and pose some open questions.
    CIRM - Chaire Jean-Morlet 2014 - Aix-Marseille Université

    11G20 - Curves over finite and local fields
    14G15 - Finite ground fields
    14H52 - Elliptic curves

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 09/10/14
      Date de captation : 19/02/14
      Sous collection : Research School
      Format : quicktime ; audio/x-aac
      arXiv category : Number Theory ; Algebraic Geometry
      Domaine : Algebra ; Number Theory
      Durée : 00:59:43
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2014-02-19_Shparlinski_part2.mp4

    Informations sur la rencontre

    Nom de la rencontre : Jean-Morlet Chair - Doctoral school : Frobenius distribution on curves / Chaire Jean-Morlet - Ecole doctorale : distribution de Frobenius sur des courbes
    Organisateurs de la rencontre : Kohel, David ; Ritzenthaler, Christophe ; Shparlinski, Igor
    Dates : 17/02/14 - 28/02/14
    Année de la rencontre : 2014
    URL Congrès : https://www.chairejeanmorlet.com/1059.html

    Citation Data

    DOI : 10.24350/CIRM.V.18598103
    Cite this video as: Shparlinski, Igor (2014). Group structures of elliptic curves #2.CIRM . Audiovisual resource. doi:10.24350/CIRM.V.18598103
    URI : http://dx.doi.org/10.24350/CIRM.V.18598103

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